Answer
The velocity is approximately -0.999774 times the speed of light (c).
Step-by-step explanation
To calculate the velocity of an object using the Doppler effect, we need to compare the observed wavelength (λ) of the object with the rest wavelength (λ₀) of the same object. The Doppler formula is given by:
λ/λ₀ = (1 + v/c)
Where:
λ = Observed wavelength
λ₀ = Rest wavelength
v = Velocity of the object
c = Speed of light
In this case, we have two observed wavelengths for the hydrogen beta line: λ₁ = 486.135 nm and λ₂ = 486.026 nm. The rest wavelength (λ₀) for the hydrogen beta line is 486.135 nm.
Let's calculate the velocity (v) using both observed wavelengths separately:
For λ = 486.135 nm:
486.135 nm / 486.135 nm = 1 + v / c
1 = 1 + v / c
v = 0
For λ = 486.026 nm:
486.026 nm / 486.135 nm = 1 + v / c
0.999774 = 1 + v / c
v / c = -0.999774
v = -0.999774 * c
Therefore, the velocity is approximately -0.999774 times the speed of light (c).
[The negative sign indicates that the object is moving towards the observer. Also, keep in mind that the units used here are nm (nanometers) for wavelengths and m/s (meters per second) for velocity.]